On the Question of Supercharging Carburetor Engines
Abstract Generated abstract
This paper examines the use of supercharging as a means of increasing the power of carburetor automobile engines when further gains from compression ratio become limited. Using a theoretical ideal cycle with forced ignition, it calculates cycle temperatures, pressures, filling coefficients, mean indicated pressure, and specific fuel consumption for inlet pressures from 0.6 to 2.2 kg/cm² and compression ratios from 4.8 to 7.2. The analysis indicates that supercharging sharply increases charge weight and mean indicated pressure, while only slightly affecting combustion temperature, but it also raises maximum cycle pressures and can slightly worsen fuel economy because compressor work exceeds the gain from positive pumping work. Compared under similar antiknock conditions, supercharging is found to increase mean indicated pressure far more than raising the compression ratio alone.
Full Text
On the Issue of Supercharging Carburetor Engines
A. M. Bakaleinik
(Presented by Prof. V. K. Nechaev, Doctor of Technical Sciences)
A characteristic feature of the engines of modern automobiles is their high power per liter, obtained as a result of increasing shaft speeds and compression ratios and improving the design.
An analysis of changes in the technical characteristics of automobile engines over a number of years makes it possible to expect a further increase in power per liter. As a result, the problem arises of using supercharging, that is, forcing the combustible mixture into the cylinders of automobile engines, since other methods—in particular, a further increase in the compression ratio—will not be able sharply to change the power characteristics of the latter.
Numerous studies show that supercharging is the most effective means of increasing engine power. However, these studies have usually been limited to slight supercharging \((1.4\text{--}1.5\ \mathrm{atm})\), since a further increase in the pressure of the mixture at the engine inlet leads to the need to reduce the compression ratio. At the same time, the question of the influence of a simultaneous change in supercharging pressure and compression ratio on engine operation is still not entirely clear. Taking into account that an experimental study of this question requires very cumbersome and complex experiments, it is advisable, as a first approximation, to consider in a theoretical cycle the influence of increasing the inlet pressure and the compression ratio on the power and economy indicators of an automobile engine with forced ignition. Studies of the theoretical cycle make it possible not only to determine the maximum attainable economy and mean pressures of a real engine, but also to obtain the necessary fundamental starting points that facilitate the experimental study of a real engine.
In carrying out the theoretical investigation of the problem posed above, it was assumed that the theoretical (ideal) engine has the following features:
the intake system has no hydraulic resistance, and when the filling process is carried out slowly (the throttle is fully open) the intake pressure is equal to the pressure downstream of the supercharger;
the combustion process proceeds at an infinitely high rate, that is, it begins and ends at the moment when the piston is at top dead center;
the compression and expansion processes are adiabatic;
the exhaust system, like the intake system, offers no resistance to the flow of gases.
In order to determine the dependence of engine power and economy on the intake pressure \(p_{\mathrm{in}}\) and the compression ratio \(\varepsilon\), a series of heat calculations was carried out for various values of \(p_{\mathrm{in}}\)—from \(0.6\) to \(2.2\ \mathrm{kg/cm^2}\) in steps of \(0.4\ \mathrm{kg/cm^2}\).
and several values of $\varepsilon$—from 4.8 to 7.2 in steps of 0.8. All calculations were carried out at an excess-air coefficient $\alpha$ equal to 0.8, which, as is known, corresponds to the maximum-power regime. The fuel is gasoline, whose properties are characterized by the following data:
elemental composition $C = 85.5\%$ and $H = 14.5\%$;
heat of combustion $h_u = 10400\ \text{kcal/kg}$;
latent heat of evaporation $r = 75\ \text{kcal/kg}$;
specific heat of liquid fuel $c_{\text{liq.f}} = 0.58\ \text{kcal}/\text{kg}^{\circ}\text{C}$;
molecular weight of the fuel vapors $m_{\text{f.v}} = 114$.
The amount of air theoretically required for the combustion of $1\ \text{kg}$ of this fuel is $l_0 = 14.95\ \text{kg/kg}$, or $L_0 = 0.513\ \text{mol/kg}$.
In order that the results of calculations of the theoretical cycle differ as little as possible from reality, it is necessary to take into account the change in the heat capacity of the gases with temperature and their dissociation at high temperature. As calculations [1] have shown, in rich mixtures dissociation is negligible, and therefore in the present case only the change in the heat capacity of the gases with temperature is taken into account.
The most important results of the thermal calculations are given below.
Cycle Temperatures
The temperature at the end of suction was determined by the formula proposed by Prof. I. M. Lenin [3], which takes into account the difference between the heat capacities of the residual gases and the fresh mixture, as well as the expansion of the residual gases during suction,
\[ T_a = \frac{ T_0 + \Delta t + \gamma \psi T_r \left(\frac{p_{\text{in}}}{p_r}\right)^{\frac{k-1}{k}} }{ 1+\gamma\psi } \ ^\circ\mathrm{K}, \tag{1} \]
where $T_r$ is the temperature of the residual gases, which is usually specified;
$p_r$ is the pressure of the exhaust gases, which in the theoretical cycle is equal to $1\ \text{kg}/\text{cm}^2$;
$\psi$ is the ratio of the mean heat capacities of the residual gases and of the fresh mixture (for a rich mixture $\psi = 1.13$).
The residual-gas coefficient $\gamma$ is determined by the following formula
\[ \gamma = \frac{T_0+\Delta t}{T_r \beta\left(\varepsilon p_{\text{in}}-p_r\right)}; \tag{2} \]
where $\beta$ is the coefficient of molecular change, equal to 1.11 (at $\alpha = 0.8$).
The quantity $\Delta t$ entering expression (2) accounts for the decrease in the temperature of the mixture during fuel evaporation and for its heating by hot engine parts. In the theoretical engine, heating by hot parts is neglected, and the temperature decrease due to fuel evaporation is determined by the formula
\[ \Delta t = \frac{x r}{\alpha l_0 c_{\text{air}} + c_{\text{liq.f}}} \ ^\circ\mathrm{C}, \tag{3} \]
where $x$ is the vapor content of the combustible mixture (for the theoretical cycle, equal to 1).
The decrease in the temperature of the combustible mixture, determined by formula (3), for the given composition is equal to 21.8°C.
The temperature at the end of compression was found from the expression
\[ T_c=T_a\varepsilon^{k_1-1}. \tag{4} \]
The temperature at the end of combustion \(T_z\) was determined from the following equation
\[ \xi(h_u-\Delta h_u)+aL_0mc_{v0}t_c'+c_{n.m}t_c' +\beta\gamma\left(aL_0+\frac{1}{m_{n.m}}\right)mc'_{vr}t_c = \]
\[ =\beta(1+\gamma)\left(aL_0+\frac{1}{m_{n.m}}\right)mc''_{vr}t_z, \tag{5} \]
where \(\xi\) is the coefficient of heat release during combustion; in the theoretical cycle \(\xi=1\);
\(\Delta h_u\) are heat losses due to the chemical incompleteness of combustion of a rich mixture, determined by the usual formula
\[ \Delta h_u=14600(1-\alpha)\ \text{kcal/kg}; \]
\(mc_{v0}\) is the mean molecular heat capacity of the fresh mixture, determined by the formula
\[ mc_{v0}=4.94+0.365\cdot10^{-3}(t_1+t_2)\ \text{kcal/mol }^\circ\text{C}; \]
\(mc_{vr}\) is the mean molecular heat capacity of the combustion products (or residual gases), taken over the corresponding temperature interval: \(mc'_{vr}\) from 0 to \(t_c'\) and \(mc''_{vr}\) from 0 to \(t_z''\); for a rich mixture \((\alpha=0.8)\) it was determined by the formula
\[ mc_{vr}=4.976+0.748\cdot10^{-3}(t_1+t_2)\ \text{kcal/mol }^\circ\text{C}. \]
To determine the temperature at the end of expansion, the usual formula was used
\[ T_e=\frac{T_z}{\varepsilon^{k_2-1}}. \tag{6} \]
The magnitude of the average values of the adiabatic exponent for compression \(k_1\) and of the adiabatic exponent for expansion \(k_2\), as calculations [1] have shown, depends only very slightly on changes in supercharging pressure and compression ratio. Therefore, to simplify the calculations, it appears possible to adopt identical average values of the adiabatic exponents for all intake pressures and compression ratios: for the compression line \(k_1=1.38\), and for the expansion line \(k_2=1.25\).
The influence of supercharging on the cycle temperatures, obtained as a result of calculations by formulas (1), (4), (5), and (6), is illustrated by the curves in Fig. 1.
The decrease in the temperature at the end of intake with increasing supercharging pressure is explained by the reduction in the relative amount of residual gases (Fig. 1) and by the constancy of the temperature of the air at the engine inlet, the compression of which in the supercharger is assumed to be isothermal. The nature of the change in the temperature at the end of compression depends directly on the change in the intake temperature, which also explains the decrease in \(T_c\) under supercharging.
Attention is drawn to the very slight change in the temperature at the end of combustion when the intake pressure is varied over a wide range—from 0.6 to 2.2 kg/cm². This is easily explained if one takes into account the peculiarity
quantitative regulation, under which the calorific value of the working mixture is preserved. The combustion temperature depends mainly on the latter.
Since, with supercharging, the relative amount of residual gases decreases, then during combustion, as the inlet pressure increases, the expenditure of heat on heating the inert part of the charge decreases, and the temperature at the end of combustion should increase. But the decrease in the relative amount of residual gases at the same time leads to a fall in the temperature at the end of compression, and therefore, in the final result, the rise in combustion temperature is insignificant. This latter circumstance also accounts for the slight increase in the temperatures at the end of expansion under supercharging.
Fig. 1
Cycle temperatures and residual-gas coefficient as functions of inlet pressure.
Filling of the engine
The filling of the engine with fresh mixture is evaluated by the filling coefficient $\eta_v$, which, as is known, is the ratio of the weight of mixture actually admitted into the engine cylinders to the weight of mixture that could fill the working volume of the cylinders at the temperature and pressure of the air (or mixture) downstream of the supercharger. When an engine operates with supercharging, the filling coefficient is determined from the following formula:
\[ \eta_v = \left( \varepsilon - \frac{p_{vp}}{T_a} - \frac{p_r}{T_r} \right) \frac{T_k}{p_k(\varepsilon - 1)}, \]
where $T_k$ and $p_k$ are the temperature and pressure of the mixture after the supercharger.
For the theoretical cycle it is expedient to present the last formula in a somewhat transformed form:
\[ \eta_v = \left( \varepsilon \frac{T_r}{T_a} - \frac{p_r}{p_{vp}} \right) \frac{p_{vp}}{p_k} \frac{T_k}{T_r} \frac{1}{\varepsilon - 1}. \]
Taking into account that in the theoretical cycle $p_{vp} = p_k$, we finally obtain:
\[ \eta_v = \left( \varepsilon \frac{T_r}{T_a} - \frac{p_r}{p_{vp}} \right) \frac{T_k}{T_r} \frac{1}{\varepsilon - 1}. \tag{7} \]
The values of the filling coefficient, determined from expression (7) and presented in Figs. 2 and 3, show that in the theoretical cycle, even in the absence of supercharging, the filling coefficient proves to be greater than unity, which is explained by the decrease in the temperature of the combustible mixture during evaporation of the fuel.
With an increase in supercharging pressure, the filling coefficient increases as a result of the decrease in the relative amount of residual gases. Po-
An increase in the compression ratio has different effects on filling when the engine operates at a partly closed throttle and under supercharging. It is known that in throttled conditions, when $\rho_r > p_{\mathrm{in}}$, the residual gases expand during the filling process, whereas under supercharging, when $p_{\mathrm{in}} > p_r$, on the contrary, they are compressed.
Fig. 2. Coefficient of filling and relative weight filling as functions of intake pressure.
Therefore, with an increase in the compression ratio, when the amount of residual gases decreases, an increase in the coefficient of filling is observed in the first case and a decrease in it in the second. At $p_{\mathrm{in}} = 1.0\ \mathrm{kg/cm^2}$ the volume
Fig. 3. Coefficient of filling as a function of compression ratio at various intake pressures.
of residual gases remains constant, and therefore a change in the compression ratio does not affect the value of the coefficient of filling.
However, the values of the coefficient of filling determined by formula (7) still do not characterize the change in weight filling under supercharging.
Let us introduce the concept of relative weight filling \(G_{\mathrm{rel}}\), representing the ratio, expressed as a percentage, of the weight of the mixture actually admitted into the engine cylinders to the weight of the mixture that could fill the working volume of the cylinders at the temperature and pressure of the surrounding medium.
According to the definition,
\[ G_{\phi}=\frac{p_k V_h}{R T_k}\eta_v \quad \text{and} \quad G_m=\frac{p_o V_h}{R T_o}. \]
Then
\[ G_{\mathrm{rel}}=\frac{G_{\phi}}{G_m} = \frac{p_k}{p_o}\cdot \frac{T_o}{T_k}\eta_v\,100\%. \]
As a result of the isothermal compression of air in the supercharger, \(T_k=T_o\); moreover, \(p_o=1.0\ \mathrm{kg/cm^2}\). Finally,
\[ G_{\mathrm{rel}}=p_k\eta_v\,100\%. \tag{8} \]
The dependence of the relative weight filling on the intake pressure, determined from expression (8), is given in Fig. 2.
Cycle Pressures
The pressures at the characteristic points of the cycle were determined from the following formulas:
compression-end pressure
\[ p_c=p_{\mathrm{in}}\varepsilon^{k_1}; \tag{9} \]
combustion-end pressure
\[ p_z=\beta p_c\frac{T_z}{T_c}; \tag{10} \]
expansion-end pressure
\[ p_e=\frac{p_z}{\varepsilon^{k_2}}. \tag{11} \]
The results of calculations using the indicated expressions (9), (10), and (11), presented in Fig. 4, show a sharp increase in cycle pressures under supercharging, which is caused by an equally sharp increase in the weight filling as the intake pressure rises (Fig. 2).
Mean Cycle Pressure
The mean pressure of the theoretical cycle, without taking into account pumping losses and the energy expended to drive the supercharger, is determined from the expression:
\[ p_t'=\frac{1}{\varepsilon-1} \left[ \frac{p_z-\varepsilon p_e}{k_2-1} - \frac{p_c-\varepsilon p_{\mathrm{in}}}{k_1-1} \right]\ \mathrm{kg/cm^2}. \tag{12} \]
With throttles partly closed, some work, or part of the mean pressure, must be expended to fill the cylinder with fresh combustible mixture; under supercharging, however, the work of charging the engine cylinders becomes positive. However, in this case, for compressing the air in the compressor
necessary expenditure of work or, per unit volume, expenditure of mean pressure. We take the compression of air in the compressor of the theoretical engine to be isothermal, since in this case the expenditure of work will be the smallest. Then
\[ L_{\text{compr}} = 2{,}303 p_{\text{in}} V_r(\varepsilon - 1)\lg \frac{p_{\text{in}}}{p_0} = 2{,}303 p_{\text{in}} V_h \lg \frac{p_{\text{in}}}{p_0} \ \frac{\text{kgm}}{\text{kg}}; \]
\[ \Delta p_{\text{compr}} = 2{,}303 p_{\text{in}} \lg \frac{p_{\text{in}}}{p_0} \ \frac{\text{kg}/\text{m}^2}{\text{kg}} . \tag{13} \]
Fig. 4. Cycle pressures as a function of intake pressure.
A summary accounting of the pumping work of the engine and of the work for compressing the air in the supercharger, expressed in terms of mean pressure, gives the results presented in Table 1.
Table 1
Summary accounting of the pumping work of the engine and the work for compressing air in the supercharger, kg/cm²
| Intake pressure, kg/cm² | Intake pressure, kg/cm² | Intake pressure, kg/cm² | Intake pressure, kg/cm² | Intake pressure, kg/cm² | |
|---|---|---|---|---|---|
| 0,6 | 1,0 | 1,4 | 1,8 | 2,2 | |
| \(\Delta p_{\text{pump}}\) | −0,4 | 0 | +0,40 | +0,80 | +1,20 |
| \(\Delta p_{\text{compr}}\) | — | — | 0,47 | 1,06 | 1,73 |
| \(\Delta p_{\text{sum}}\) | −0,4 | 0 | −0,07 | −0,26 | −0,53 |
It follows from Table 1 that the expenditure of mean pressure on compressing the air in the supercharger exceeds the increase in mean pressure due to pumping work under supercharging. This circumstance must, naturally, lead to some deterioration of economy under supercharging.
The mean indicated pressure \(p_t\) of the theoretical cycle (Fig. 5), calculated by formula (12) and corrected for the pumping work of the engine and for the expenditure of work on compressing the air in the supercharger, increases sharply with increasing intake pressure and considerably less with increasing compression ratio.
Fig. 5. Mean indicated pressure as a function of intake pressure and compression ratio.
Specific fuel consumptions
The specific fuel consumptions are determined by the following formula
\[ g_t = 270 \cdot 10^6 \frac{p_k \eta_v}{R T_k p_t (a l_0 + 1)} \ \text{g/hp·h}. \]
We take the gas constant for all mixture qualities equal to 28. Substituting the known quantities, we finally obtain
\[ g_t = 33.5 \cdot 10^3 \frac{p_k}{14.95\alpha + 1}\frac{\eta_v}{p_t}\ \text{g/hp·h}. \tag{14} \]
The specific fuel consumptions corresponding to the corrected mean indicated pressure \(p_t\) and found from expression (14) are given in Fig. 6. The increase in specific fuel consumption under throttling
is associated with an increase in pumping losses. A certain decrease in economy under supercharging is explained by the excess expenditure of work for compressing the air over the additional work obtained as a result of the excess intake pressure.
To analyze the question of the most effective ways of uprating an engine, it is necessary to compare the results of increasing the compression ratio and the supercharging pressure, bearing in mind that changes in the latter must take place within limits comparable from the standpoint of antiknock resistance.
Fig. 6. Specific fuel consumption as a function of intake pressure and compression ratio.
fuel, limits. It may be assumed that the requirements imposed on the octane number of the fuel are to a considerable extent determined by the state of the combustible mixture at the beginning of combustion [2]. In connection with this, in our case the operating conditions with supercharging at \(p_{\mathrm{in}} = 1.8\) ata, with a compression ratio \(\varepsilon = 4.8\), and operation without supercharging with the compression ratio raised to 7.2 are quite comparable. And indeed, it follows from Table 2 that in both cases the pressures at the end of compression are practically the same, while the temperature at the end of compression in the first case (with supercharging) is even lower than in the second.
The calculation data for the theoretical engine, presented in Table 2, show that uprating the engine by means of supercharging is considerably more effective than by increasing the compression ratio. At the same time
since supercharging makes it possible almost to double the mean indicated pressure, an increase in the compression ratio (within comparable limits) gives an increase in mean indicated pressure of only 20%. This circumstance is important because a further increase in the compression ratio gives, as is known, an even smaller increase in mean indicated pressure.
It should be noted that the use of supercharging is associated with a significant increase in the maximum cycle pressure, as well as with some deterioration in the economy even of the theoretical cycle.
Table 2
Effect of supercharging and compression ratio on the parameters of the theoretical cycle
| Cycle parameters | Initial regime $p_{\mathrm{in}} = 1.0$ atm, $\varepsilon = 4.8$ |
Comparable regimes $p_{\mathrm{in}} = 1.8$ atm, $\varepsilon = 4.8$ absolute value |
Comparable regimes $p_{\mathrm{in}} = 1.8$ atm, $\varepsilon = 4.8$ in % of initial regime |
Comparable regimes $p_{\mathrm{in}} = 1.0$ atm, $\varepsilon = 7.2$ absolute value |
Comparable regimes $p_{\mathrm{in}} = 1.0$ atm, $\varepsilon = 7.2$ in % of initial regime |
|---|---|---|---|---|---|
| $p_c$, kg/cm$^2$ | 8.7 | 15.6 | 179 | 15.2 | 175 |
| $T_c$, °K | 580 | 540 | 93 | 630 | 108 |
| $T_z$, °K | 2760 | 2775 | 100 | 2822 | 102 |
| $p_z$, kg/cm$^2$ | 46.0 | 89.0 | 193 | 76.1 | 165 |
| $T_e$, °K | 1865 | 1875 | 100 | 1723 | 92 |
| $p_e$, kg/cm$^2$ | 6.5 | 12.5 | 192 | 6.4 | 98 |
| $p_t$, kg/cm$^2$ | 13.0 | 25.2 | 194 | 15.6 | 120 |
| $g_t$, g/hp·h | 214.0 | 216.2 | 101 | 179.0 | 84 |
Literature
- Bakaleinik A. M. Study of the influence of supercharging on the operation of an automobile carburetor engine (Candidate dissertation). MAMI, 1951.
- Beckman V. V. Design and dynamics of racing automobiles. Mashgiz, 1947.
- Lenin I. M. Working processes and carburetion in automobile engines. Mashgiz, 1947.